Word (.docx)
Acrobat (.pdf)
Examples
can be represented as 
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Clarifications
Clarification 1: Instruction emphasizes conceptual understanding through the use of manipulatives or visual models, including circle graphs, to represent fractions.Clarification 2: Denominators are limited to 2, 3, 4, 5, 6, 8, 10 and 12.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Number Line
- Circle Graph
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
- During instruction, teachers should have students practice representing fractions using manipulatives (e.g., fraction strips, circles, relationship rods), visual area models (e.g., partitioned shapes) and on a number line. Manipulatives, visual models and number lines must extend beyond 1 so that students can represent fractions greater than one (MTR.2.1, MTR.5.1).
- In instruction of MA.3.FR.1.1, students learn that unit fractions are the foundation for all fractions. MA.3.FR.1.2 builds understanding that all fractions, including fractions equal to and greater than one, decompose as the sum of unit fractions.
- In understanding fractions are numbers, students make connections about whole number operations that will allow them to perform operations with fractions in later grades. For example, understanding fractions as numbers allows students to reason that + = in Grade 4 because we are adding together a total of 4 parts that are each one-third in size (MTR.5.1).
Common Misconceptions or Errors
- Students can misconceive that fractions equal to and greater than 1 can also be represented as the sum of unit fractions (e.g., = + + + + ). Flexible representations of models (e.g., rectangular area models that align with number lines) help students connect their understanding of fractions and how they are decomposed into unit fractions.
Strategies to Support Tiered Instruction
- Instruction includes modeling how fractions are decomposed. Using fraction circles, students build and then see that there are 4 pieces that make up the whole circle.
- Example:
- Instruction includes more than one model so that students can experience and connect fractions in multiple ways. Flexible representations of models (e.g., rectangular area models that align with number lines) help students connect their understanding of fractions and how they are decomposed into unit fractions.
- Example:
- Students then apply this understanding to fractions greater than one. Using fraction circles, students build and then see that there are 8 pieces that make up
two whole circles.
- Example:
- Instruction includes folding and/or cutting pre-made shapes into halves. Students physically bend the paper into halves and then label the pieces. Instruction includes relating the pieces back to the numerator and denominator and then connecting it to the equation. Using multiple shapes with the same denominators will solidify basic fraction understanding. Instruction should progress with other denominators.
- Example:
Instructional Tasks
Instructional Task 1
- Part A. How many one-fifth sized parts are added together to equal 1 whole? Prove your thinking with a visual model or number line.
- Part B. How many one-fifth sized parts are added together to equal 2 wholes? Prove your thinking with a visual model or number line.
- Part A. Model two wholes divided into tenths.
- Part B. Write an equation to match your model.
- Part C. What would happen to your equation if you added another whole?
Instructional Items
Instructional Item 1Create an equation to represent the total number of one-fourth sized pieces in 3 wholes.
Instructional Item 2
Represent the fraction 8/3 as the sum of unit fractions.Instructional Item 3
Which of the following expressions models 7/4 ?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Image/Photograph
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Ideas
Virtual Manipulative
MFAS Formative Assessments
Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.
Students are read a word problem about a wall being painted and asked to describe what three-eighths of the wall means.
Students are read a word problem about a student who has run three-fourths of a race and asked to describe what that means.
Original Student Tutorials Mathematics - Grades K-5
Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.
Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.
Student Resources
Original Student Tutorials
Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.
Type: Original Student Tutorial
Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.
Type: Original Student Tutorial
Virtual Manipulative
This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:
- Build equivalent fractions using numbers and pictures.
- Compare fractions using numbers and patterns
- Recognize equivalent simplified and unsimplified fractions
Type: Virtual Manipulative
Parent Resources
Image/Photograph
Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.
Type: Image/Photograph
Virtual Manipulative
This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.
Some of the sample learning goals can be:
- Build equivalent fractions using numbers and pictures.
- Compare fractions using numbers and patterns
- Recognize equivalent simplified and unsimplified fractions
Type: Virtual Manipulative
